1 . 已知数列
的前
项和为
,
.
(1)求
的值;
(2)证明数列
是等比数列,并求出数列
的通项公式;
(3)数列
中是否存在三项,它们可以构成等差数列?(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb6457669c73995424232d9ef67983b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e616142cd7122cb7c4e9bc46bb7394.png)
(2)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17d72d1d20d385920c3d9da6bed8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
2 .
个有次序的实数
所组成的有序数组
称为一个
维向量,其中
称为该向量的第
个分量.特别地,对一个
维向量
,若
,称
为
维信号向量.设
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在14个两两垂直的14维信号向量.
(3)已知
个两两垂直的2024维信号向量
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9843b6a3f1c106c363471ea2d77263cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6bc224faf837b27fdfc53671240644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e74dc6e97cc8aceb97dca8985ba36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657004273c12e063197e218be4f37852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b800dbadd54944fb6b88e01771188a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40b9b6b5299fe81645fbc71ea40d9cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d43cafa129d60c58d0f913cc006206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cfce6ff54e403e1486244d51395bed.png)
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在14个两两垂直的14维信号向量.
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aaf5adce57da3463ab8c7f55ea444c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
2023-11-15更新
|
237次组卷
|
4卷引用:北京市北京师范大学附属中学2023-2024学年高二上学期数学期中考试数学试题
北京市北京师范大学附属中学2023-2024学年高二上学期数学期中考试数学试题北京市第十一中学2023-2024学年高一下学期期中练习数学试卷(已下线)模块三 专题2 专题1 平面向量运算(已下线)模块三 专题2 解答题分类练 专题3 平面向量各类运算(解答题)
名校
解题方法
3 . 已知椭圆C:
的离心率为
长轴的右端点为
.
(1)求C的方程;
(2)不经过点A的直线
与椭圆C分别相交于
两点,且以MN为直径的圆过点
,
①试证明直线
过一定点,并求出此定点;
②从点
作
垂足为
,点
写出
的最小值(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a0b452fd57bbdc105589e871baa009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba447f2abb9bd37cc8d3f607f7e694a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de255124598a717187ee85cb944be05.png)
(1)求C的方程;
(2)不经过点A的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
①试证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7920d2550a6af7df3db60a33fe02c53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68967218fdc94c817f0e3b380cce22c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60436c1f7b5c2f6b5331548216e8077.png)
您最近一年使用:0次
名校
4 . n个有次序的实数
,
,
,
所组成的有序数组
称为一个n维向量,其中
称为该向量的第
个分量.特别地,对一个n维向量
,若
,
,称
为n维信号向量.设
,
,
则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在14个两两垂直的14维信号向量.
(3)已知k个两两垂直的2024维信号向量
,
,
,
满足它们的前m个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee470d0232b6b37f2fb2ab15aae0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d5cd21ff3c760e7ec3130f5bfa8c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da796531c7b6c590a22b811df1fcef53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0cf905f1d4af294ebc9c19facd64c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d5cd21ff3c760e7ec3130f5bfa8c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a414d372b680499f1c8ca1a7ae5f4d82.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd04a2f39ff6f36e9531bac16960d71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c7c807358869b70becd16ca80e1714.png)
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在14个两两垂直的14维信号向量.
(3)已知k个两两垂直的2024维信号向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
5 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5734d093f305e687e303a62a6860f790.png)
.
(1)当
时,证明
;
(2)若直线
是曲线
的切线,设
,求证:对任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e54f38c13f26cd12acfbebecc83c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5734d093f305e687e303a62a6860f790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae676c936b91af769360c2624f70e532.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d97556ab3ec460995e88a7343a3e356.png)
您最近一年使用:0次
2023-07-09更新
|
460次组卷
|
3卷引用:北京市朝阳区2022-2023学年高二下学期期末质量检测数学试题
名校
6 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)设
,求证:当
时,
;
(3)对任意的
,判断
与
的大小关系,并证明结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38e2cfb9e16f2f5d7a1e9a7590dd073.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585de67a3fc494297d375d339af6d153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b79ae1ceee652b06fc889607ff3f1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa38ca27c6c0c40d5e36b2ae4fb7ba7.png)
(3)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c975a637794e6be6dd95e1e1ba12620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa9fca7538f46d9d2b4429dd085ac78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
您最近一年使用:0次
2023-06-18更新
|
428次组卷
|
2卷引用:北京市大兴区2022-2023学年高二下学期期中考试数学试题
名校
7 . 设A为非空集合,令
,则
的任意子集R都叫做从A到A的一个关系(Relation),简称A上的关系.例如
时,
{0,2},![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76986e6f96cbb9d7d6d0fbcf0bf2321a.png)
,
,
{(0,0),(2,1)}等都是A上的关系.设R为非空集合A上的关系.给出如下定义:
①(自反性)若
,有
,则称R在A上是自反的;
②(对称性)若
,有
,则称R在A上是对称的;
③(传递性)若
,有
,则称R在A上是传递的;
如果R同时满足这3条性质,则称R为A上的等价关系.
(1)已知
,按要求填空:
①用列举法写出
______________________;
②A上的关系有____________个(用数值做答);
③用列举法写出A上的所有等价关系:{(0,0),(1,1),(2,2)},{(0,0),(1,1),(2,2),(0,1),(1,0)},{(0,0),(1,1),(2,2),(0,2),(2,0)},_______________,_______________,共5个.
(2)设
和
是某个非空集合A上的关系,证明:
①若
,
是自反的和对称的,则
也是自反的和对称的;
②若
,
是传递的,则
也是传递的.
(3)若给定的集合A有n个元素(
),
,
,...,
为A的非空子集,满足
且两两交集为空集.求证:
为A上的等价关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff994543fe18b563c7127c8b2a874358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5689e50a9353ba69ff5b71e7b6a3c795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8225d0531fba46cbb4a3af4dd2d6751f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76986e6f96cbb9d7d6d0fbcf0bf2321a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c06ed271ff0a6407a3bf5deec5871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934909fce1b90557163c6f43d4f0790d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8225d0531fba46cbb4a3af4dd2d6751f.png)
①(自反性)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd170c506a8ce70f550f5751ae016ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e96fb327d44b08d715e86db04cc9785.png)
②(对称性)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328ae22ec119ce8f0faac8dc554a2c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c950781f08495bc2a4c20454c26c48d8.png)
③(传递性)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227539cbcd96eb67cbcf7c94de56598d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78dd7c7d34bcfcae1f423a684aae9542.png)
如果R同时满足这3条性质,则称R为A上的等价关系.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5689e50a9353ba69ff5b71e7b6a3c795.png)
①用列举法写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b0949c177d28fe5b6ec4a0de58c80a.png)
②A上的关系有____________个(用数值做答);
③用列举法写出A上的所有等价关系:{(0,0),(1,1),(2,2)},{(0,0),(1,1),(2,2),(0,1),(1,0)},{(0,0),(1,1),(2,2),(0,2),(2,0)},_______________,_______________,共5个.
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc18a5bb2e53586331b2a58538a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc18a5bb2e53586331b2a58538a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05725d20ff805152beff52c7a5e8d735.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc18a5bb2e53586331b2a58538a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7077a5e7dce0e2f0e678b1147deae46.png)
(3)若给定的集合A有n个元素(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4bae4bf0e8cf84b9e1c6c7258b06d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79ff32c9e80fd90fcdb360f9a5a21c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591eaeea196d5720d0762ced03e8ce3b.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)求证:当
时,
;
(2)设斜率为
的直线与曲线
交于两点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
(1)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab32224dfeba4536a75cfc0aa9eab7d2.png)
(2)设斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35115e581c859d8fd22653883ebd35ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d06595c7d839f2edbf9ef575ef027d6.png)
您最近一年使用:0次
2021-08-04更新
|
673次组卷
|
3卷引用:北京市大兴区2020-2021学年高二下学期期末数学试题
北京市大兴区2020-2021学年高二下学期期末数学试题安徽省六安市舒城中学2022届高三下学期一模理科数学试题(已下线)湖北省武汉市(武汉六中)部分重点中学2024届高三第二次联考数学试题变式题17-22
9 . 若有穷数列
满足
且对任意的
,
至少有一个是数列
中的项,则称数列
具有性质![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断数列1,2,4,8是否具有性质P,并说明理由;
(2)设项数为
的数列
具有性质
,求证:
;
(3)若项数为
的数列
具有性质
,写出一个当
时,
不是等差数列的例子,并证明当
时,数列
是等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b96f565b4ca625ab41a782e3dfd0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0492686dc1959ba361d9b2832491620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e72ad2e72453867d089770c3f4c63da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断数列1,2,4,8是否具有性质P,并说明理由;
(2)设项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3411ddca520e2bcb516d0c5c0832aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee349b3f104aa5a5e03830a205570f3.png)
(3)若项数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3411ddca520e2bcb516d0c5c0832aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0266e0e890fb1b84be352fdc65bb298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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2020-12-25更新
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587次组卷
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6卷引用:北京市第五十五中学2022-2023年高二下学期3月调研数学试题
北京市第五十五中学2022-2023年高二下学期3月调研数学试题(已下线)专题05 《数列》中的解答题压轴题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)上海市嘉定区2021届高三上学期一模数学试题(已下线)重难点01 数列(基本通项求法)-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)考向17 数列新定义-备战2022年高考数学一轮复习考点微专题(上海专用)
名校
10 . 已知M是由满足下述条件的函数构成的集合:对任意
,①方程
有实数根;②函数
的导数
满足
.
(1)判断函数
是集合M中的元素,并说明理由;
(2)集合M中的元素
具有下面的性质:若
的定义域为D,则对于任意
,都存在
,使得等式
成立.试用这一性质证明:方程
有且只有一个实数根;
(3)对任意
,且
,求证:对于
定义域中任意的
,
,
,当
,且
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cac663990f61a4a3086c6bea3d51f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4b85c070b9511e29c2677728f425c5.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1994b5f36e31a7d78bea39f6e71fcfc7.png)
(2)集合M中的元素
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5313c921defe84689aefde4773ad2b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26597a94b1f024b0f75bb1bd76ccc4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d0efbfaf649d6ff75ad91f3a69b423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
(3)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57cac663990f61a4a3086c6bea3d51f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b7e150af2052a1664cde963273d905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42367830867a96861460aebfd53a0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a385a2c08126b919ebf35e4121595842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc10d2a4a6a6d6cb8014cd7312f16053.png)
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